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arXiv · 0904.2194

Root polytopes, triangulations, and the subdivision algebra, I

Karola Meszaros
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Abstract

The type A_n full root polytope is the convex hull in R^{n+1} of the origin and the points e_i-e_j for 1<= i x_{ik}x_{ij}+x_{jk}x_{ik}+βx_{ik}, can be interpreted as triangulations of P(T). Using these triangulations, the volume and Ehrhart polynomial of P(T) are obtained. If we allow variables x_{ij} and x_{kl} to commute only when i, j, k, l are distinct, then the reduced form of m[T] is unique and yields a canonical triangulation of P(T) in which each simplex corresponds to a noncrossing alternating forest. Most generally, the reduced forms of all monomials in the noncommutative case are unique.

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Karola Meszaros. 2009-09-02. Root polytopes, triangulations, and the subdivision algebra, I. https://arxiv.org/abs/0904.2194

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